Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer

TL;DR

This paper provides a comprehensive method for simulating fundamental lattice gauge theories, including quantum electrodynamics and chromodynamics, on a universal quantum computer, with detailed resource estimates.

Contribution

It introduces an instruction-by-instruction protocol for simulating U(1), SU(2), and SU(3) lattice gauge theories on quantum computers, including resource analysis.

Findings

Simulation of lattice gauge theories in any dimension is feasible with specified quantum resources.

Resource scaling is characterized by  O(T^{3/2} N^{3/2} b3 / psilon^{1/2}) T gates.

Provides a practical framework for quantum simulation of fundamental physics theories.

Abstract

It is widely anticipated that a large-scale quantum computer will offer an evermore accurate simulation of nature, opening the floodgates for exciting scientific breakthroughs and technological innovations. Here, we show a complete, instruction-by-instruction rubric to simulate U(1), SU(2), and SU(3) lattice gauge theories on a quantum computer. These theories describe quantum electrodynamics and chromodynamics, the key ingredients that form the fabric of our universe. We further provide a concrete estimate of the quantum computational resources required for an accurate simulation of lattice gauge theories using a second-order product formula. We show that lattice gauge theories in any spatial dimension can be simulated using $\tilde{O}(T^{3/2}N^{3/2}\Lambda/\epsilon^{1/2})$ T gates, where $N$ is the number of lattice sites, $\Lambda$ is the bosonic gauge field truncation, and $T$ is the simulation time.